A parameter optimization approach to robust PI-controller design for systems with interval plants

The purpose of this paper is to develop an analytic way for designing optimal PI-controllers for the interval plant family. Optimality means that the coefficient intervals of the plant stabilized by a PI-controller is maximized. It will be shown that the optimization problem can be formulated in terms of an eigenvalue minimization problem of matrix pairs of the form （H（h0, g0）, H（δ1,k, δ2,k））, where k= 1, 2, 3, 4 and both H（h0, g0） and H（δ1,k,δ2,k） are frequency independent Hurwitz-like matrices. A numerical example is provided to illustrate that optimal controller parameters can be successfully obtained by a two-dimensional search.

Stability analysis of T-S fuzzy control systems with interval plants

The stability of a type of Takagi-Sugeno ( T-S) fuzzy control systems is considered. The plant of T-S fuzzy system has parameter uncertainties. By using the off-axis circle criterion and Kharitonov Theorem,a sufficient condition is derived to analyze the global asymptotic stability of T-S fuzzy control system. The proposed method has a graphical explanation which facilitates stability analysis. A numerical example is also given to demonstrate how to use our approach in analyzing certain T-S fuzzy control systems.

Optimal Robust Control for Unstable Delay System

Proportional-Integral-Derivative control system has been widely used in industrial applications.For uncertain and unstable systems,tuning controller parameters to satisfy the process requirements is very challenging.In general,the whole system’s performance strongly depends on the controller’s efficiency and hence the tuning process plays a key role in the system’s response.This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches.In this study,the Generalized Kharitonov Theorem(GKT)for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay.Using a constructive procedure based on the Hermite-Biehler theorem,we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system.Genetic Algorithms(GAs)are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties.Specifically,the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE,the Integral-Square-Error ISE,the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE.The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.

Stability margin of uncertain control systems

Achieving stability is the essential issue in the control system design. In this paper, four approaches that can be used to calculate the stability margin of the interval plant family are summarized and compared. The μ approach gives the bounds of the stability margin, and good estimation can be obtained with the numerical method. The eigenvalue approach yields accurate value, and the MATLAB＇s function robuststab sometimes provides wrong results. Since the eigenvalue approach is both accurate and computationally efficient, it is recommended for the calculation of the stability margin, while utilization of the function robuststab should be avoided due to the unreliable results it gives.